In this paper, we focus on the imprints of spatial covariant gravities on the propagation of GWs, produced by the coalescence of compact binaries, and their observational constraints with observational data of GW events from LIGO/Virgo/KAGRA collaboration. Decomposing the GWs into the left-hand and right-hand circular polarization modes, we find that the equation of motions of GWs in spatial copvariant gravities can be exactly mapped to the parametrized propagation equation proposed in [1]}, [2]}. Depending on different terms in the gravitational action of spatial covariant gravities, the new effects beyond GR can be fully characterized by four parameters: \(\bar{\nu }\) , \(\bar{\mu }\) , \(\nu _A\)  and \(\mu _A\) . The parameters \(\nu _A\)  and \(\mu _A\)  label the effects of the parity violating terms in the spatial covariant gravities, and \(\bar{\nu }\)  and \(\bar{\mu }\)  describe the effects of other possible modifications which are not relevant to parity violation. The correspondence between different terms in the spatial covariant gravities and the four parameters are sumarrized in Table. REF .
